CC3 (Ch. 4) Linear Relationships

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be described by a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change between the two variables. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

How can you represent linear relationships?

Back

Linear relationships can be represented using verbal descriptions, equations, graphs, and tables.

Front

What is the equation of a line with a slope of 2 and a y-intercept of 3?

Back

The equation is y = 2x + 3.

Front

If a line passes through the points (1, 3) and (2, 5), what is the slope?

Back

The slope is 2, calculated as (5 - 3) / (2 - 1).

Front

What is the constant rate of change in a linear relationship?

Back

The constant rate of change is the same as the slope of the line, indicating how much y changes for each unit increase in x.

Front

How do you find the equation of a line given two points?

Back

First, calculate the slope using the formula (y2 - y1) / (x2 - x1). Then, use the point-slope form y - y1 = m(x - x1) to find the equation.

Front

What does it mean if a linear equation has a negative slope?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship between the two variables.

Front

What is a table of values in relation to linear relationships?

Back

A table of values lists pairs of x and y values that satisfy a linear equation, showing how y changes with x.